Necessary and Sufficient Stability Conditions for the Case of Dependent Additive Perturbations

摘要

It is shown that nondiagonal transformations afford the extra degrees of freedom required for the attainment of Principal Direction Alignment (PDA). The associated results give a necessary and sufficient stability condition, for the case of dependent perturbations. Nonsimilarity operations where the stability results have a direct geometric interpretation in terms of the plant and perturbations matrices are considered. Necessary and sufficient stability conditions for the general case in the context of similarity operations are derived. The optimal choice of these similarity transformations requires the solution of a minimization problem, which by major PDA arguments, is shown to be convex. Thus any standard optimization technique produces reliable results.